cp's OEIS Frontend

A373120 Number of distinct possible binary ranks of integer partitions of n, where the binary rank of a partition y is given by Sum_i 2^(y_i-1).

%I A373120 #7 May 27 2024 07:14:03
%S A373120 1,1,1,2,3,4,6,8,11,15,20,26,33,43,55,70,89,109,136,167,206,251,306,
%T A373120 371,445,535,639,759,904,1069,1262,1489,1747,2047,2390,2784,3237,3754,
%U A373120 4350,5027,5798,6680,7671,8808,10091,11543,13190,15040,17128,19477,22118
%N A373120 Number of distinct possible binary ranks of integer partitions of n, where the binary rank of a partition y is given by Sum_i 2^(y_i-1).
%e A373120 The partitions of 4 are (4), (3,1), (2,2), (2,1,1), (1,1,1,1), with respective binary ranks 8, 5, 4, 4, 4, so a(4) = 3.
%t A373120 Table[Length[Union[Total[2^(#-1)]&/@IntegerPartitions[n]]],{n,0,15}]
%Y A373120 The strict case is A000009.
%Y A373120 A048675 gives binary rank of prime indices, distinct A087207.
%Y A373120 A118462 lists binary ranks of strict integer partitions, row sums A372888.
%Y A373120 A277905 groups all positive integers by binary rank of prime indices.
%Y A373120 A372890 adds up binary ranks of integer partitions.
%Y A373120 Binary indices (A048793):
%Y A373120 - length A000120, complement A023416
%Y A373120 - min A001511, opposite A000012
%Y A373120 - max A029837 or A070939, opposite A070940
%Y A373120 - sum A029931, product A096111
%Y A373120 - reverse A272020
%Y A373120 - complement A368494, sum A359400
%Y A373120 - opposite complement A371571, sum A359359
%Y A373120 - opposite A371572, sum A230877
%Y A373120 Cf. A000041, A018819, A158704, A158705, A225620, A231204, A372688.
%K A373120 nonn
%O A373120 0,4
%A A373120 _Gus Wiseman_, May 26 2024